xref: /petsc/src/ts/tutorials/advection-diffusion-reaction/reaction_diffusion.c (revision 9566063d113dddea24716c546802770db7481bc0)

#include "reaction_diffusion.h"
#include <petscdm.h>
#include <petscdmda.h>

/*F
     This example is taken from the book, Numerical Solution of Time-Dependent Advection-Diffusion-Reaction Equations by
      W. Hundsdorf and J.G. Verwer,  Page 21, Pattern Formation with Reaction-Diffusion Equations
\begin{eqnarray*}
        u_t = D_1 (u_{xx} + u_{yy})  - u*v^2 + \gamma(1 -u)           \\
        v_t = D_2 (v_{xx} + v_{yy})  + u*v^2 - (\gamma + \kappa)v
\end{eqnarray*}
    Unlike in the book this uses periodic boundary conditions instead of Neumann
    (since they are easier for finite differences).
F*/

/*
   RHSFunction - Evaluates nonlinear function, F(x).

   Input Parameters:
.  ts - the TS context
.  X - input vector
.  ptr - optional user-defined context, as set by TSSetRHSFunction()

   Output Parameter:
.  F - function vector
 */
PetscErrorCode RHSFunction(TS ts,PetscReal ftime,Vec U,Vec F,void *ptr)
{
  AppCtx         *appctx = (AppCtx*)ptr;
  DM             da;
  PetscInt       i,j,Mx,My,xs,ys,xm,ym;
  PetscReal      hx,hy,sx,sy;
  PetscScalar    uc,uxx,uyy,vc,vxx,vyy;
  Field          **u,**f;
  Vec            localU;

  PetscFunctionBegin;
  PetscCall(TSGetDM(ts,&da));
  PetscCall(DMGetLocalVector(da,&localU));
  PetscCall(DMDAGetInfo(da,PETSC_IGNORE,&Mx,&My,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE));
  hx = 2.50/(PetscReal)Mx; sx = 1.0/(hx*hx);
  hy = 2.50/(PetscReal)My; sy = 1.0/(hy*hy);

  /*
     Scatter ghost points to local vector,using the 2-step process
        DMGlobalToLocalBegin(),DMGlobalToLocalEnd().
     By placing code between these two statements, computations can be
     done while messages are in transition.
  */
  PetscCall(DMGlobalToLocalBegin(da,U,INSERT_VALUES,localU));
  PetscCall(DMGlobalToLocalEnd(da,U,INSERT_VALUES,localU));

  /*
     Get pointers to vector data
  */
  PetscCall(DMDAVecGetArrayRead(da,localU,&u));
  PetscCall(DMDAVecGetArray(da,F,&f));

  /*
     Get local grid boundaries
  */
  PetscCall(DMDAGetCorners(da,&xs,&ys,NULL,&xm,&ym,NULL));

  /*
     Compute function over the locally owned part of the grid
  */
  for (j=ys; j<ys+ym; j++) {
    for (i=xs; i<xs+xm; i++) {
      uc        = u[j][i].u;
      uxx       = (-2.0*uc + u[j][i-1].u + u[j][i+1].u)*sx;
      uyy       = (-2.0*uc + u[j-1][i].u + u[j+1][i].u)*sy;
      vc        = u[j][i].v;
      vxx       = (-2.0*vc + u[j][i-1].v + u[j][i+1].v)*sx;
      vyy       = (-2.0*vc + u[j-1][i].v + u[j+1][i].v)*sy;
      f[j][i].u = appctx->D1*(uxx + uyy) - uc*vc*vc + appctx->gamma*(1.0 - uc);
      f[j][i].v = appctx->D2*(vxx + vyy) + uc*vc*vc - (appctx->gamma + appctx->kappa)*vc;
    }
  }
  PetscCall(PetscLogFlops(16.0*xm*ym));

  /*
     Restore vectors
  */
  PetscCall(DMDAVecRestoreArrayRead(da,localU,&u));
  PetscCall(DMDAVecRestoreArray(da,F,&f));
  PetscCall(DMRestoreLocalVector(da,&localU));
  PetscFunctionReturn(0);
}

PetscErrorCode RHSJacobian(TS ts,PetscReal t,Vec U,Mat A,Mat BB,void *ctx)
{
  AppCtx         *appctx = (AppCtx*)ctx;     /* user-defined application context */
  DM             da;
  PetscInt       i,j,Mx,My,xs,ys,xm,ym;
  PetscReal      hx,hy,sx,sy;
  PetscScalar    uc,vc;
  Field          **u;
  Vec            localU;
  MatStencil     stencil[6],rowstencil;
  PetscScalar    entries[6];

  PetscFunctionBegin;
  PetscCall(TSGetDM(ts,&da));
  PetscCall(DMGetLocalVector(da,&localU));
  PetscCall(DMDAGetInfo(da,PETSC_IGNORE,&Mx,&My,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE));

  hx = 2.50/(PetscReal)Mx; sx = 1.0/(hx*hx);
  hy = 2.50/(PetscReal)My; sy = 1.0/(hy*hy);

  /*
     Scatter ghost points to local vector,using the 2-step process
        DMGlobalToLocalBegin(),DMGlobalToLocalEnd().
     By placing code between these two statements, computations can be
     done while messages are in transition.
  */
  PetscCall(DMGlobalToLocalBegin(da,U,INSERT_VALUES,localU));
  PetscCall(DMGlobalToLocalEnd(da,U,INSERT_VALUES,localU));

  /*
     Get pointers to vector data
  */
  PetscCall(DMDAVecGetArrayRead(da,localU,&u));

  /*
     Get local grid boundaries
  */
  PetscCall(DMDAGetCorners(da,&xs,&ys,NULL,&xm,&ym,NULL));

  stencil[0].k = 0;
  stencil[1].k = 0;
  stencil[2].k = 0;
  stencil[3].k = 0;
  stencil[4].k = 0;
  stencil[5].k = 0;
  rowstencil.k = 0;
  /*
     Compute function over the locally owned part of the grid
  */
  for (j=ys; j<ys+ym; j++) {
    stencil[0].j = j-1;
    stencil[1].j = j+1;
    stencil[2].j = j;
    stencil[3].j = j;
    stencil[4].j = j;
    stencil[5].j = j;
    rowstencil.k = 0; rowstencil.j = j;
    for (i=xs; i<xs+xm; i++) {
      uc = u[j][i].u;
      vc = u[j][i].v;

      /*      uxx       = (-2.0*uc + u[j][i-1].u + u[j][i+1].u)*sx;
      uyy       = (-2.0*uc + u[j-1][i].u + u[j+1][i].u)*sy;

      vxx       = (-2.0*vc + u[j][i-1].v + u[j][i+1].v)*sx;
      vyy       = (-2.0*vc + u[j-1][i].v + u[j+1][i].v)*sy;
       f[j][i].u = appctx->D1*(uxx + uyy) - uc*vc*vc + appctx->gamma*(1.0 - uc);*/

      stencil[0].i = i; stencil[0].c = 0; entries[0] = appctx->D1*sy;
      stencil[1].i = i; stencil[1].c = 0; entries[1] = appctx->D1*sy;
      stencil[2].i = i-1; stencil[2].c = 0; entries[2] = appctx->D1*sx;
      stencil[3].i = i+1; stencil[3].c = 0; entries[3] = appctx->D1*sx;
      stencil[4].i = i; stencil[4].c = 0; entries[4] = -2.0*appctx->D1*(sx + sy) - vc*vc - appctx->gamma;
      stencil[5].i = i; stencil[5].c = 1; entries[5] = -2.0*uc*vc;
      rowstencil.i = i; rowstencil.c = 0;

      PetscCall(MatSetValuesStencil(A,1,&rowstencil,6,stencil,entries,INSERT_VALUES));
      if (appctx->aijpc) {
        PetscCall(MatSetValuesStencil(BB,1,&rowstencil,6,stencil,entries,INSERT_VALUES));
      }
      stencil[0].c = 1; entries[0] = appctx->D2*sy;
      stencil[1].c = 1; entries[1] = appctx->D2*sy;
      stencil[2].c = 1; entries[2] = appctx->D2*sx;
      stencil[3].c = 1; entries[3] = appctx->D2*sx;
      stencil[4].c = 1; entries[4] = -2.0*appctx->D2*(sx + sy) + 2.0*uc*vc - appctx->gamma - appctx->kappa;
      stencil[5].c = 0; entries[5] = vc*vc;
      rowstencil.c = 1;

      PetscCall(MatSetValuesStencil(A,1,&rowstencil,6,stencil,entries,INSERT_VALUES));
      if (appctx->aijpc) {
        PetscCall(MatSetValuesStencil(BB,1,&rowstencil,6,stencil,entries,INSERT_VALUES));
      }
      /* f[j][i].v = appctx->D2*(vxx + vyy) + uc*vc*vc - (appctx->gamma + appctx->kappa)*vc; */
    }
  }

  /*
     Restore vectors
  */
  PetscCall(PetscLogFlops(19.0*xm*ym));
  PetscCall(DMDAVecRestoreArrayRead(da,localU,&u));
  PetscCall(DMRestoreLocalVector(da,&localU));
  PetscCall(MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY));
  PetscCall(MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY));
  PetscCall(MatSetOption(A,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE));
  if (appctx->aijpc) {
    PetscCall(MatAssemblyBegin(BB,MAT_FINAL_ASSEMBLY));
    PetscCall(MatAssemblyEnd(BB,MAT_FINAL_ASSEMBLY));
    PetscCall(MatSetOption(BB,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE));
  }
  PetscFunctionReturn(0);
}

/*
   IFunction - Evaluates implicit nonlinear function, xdot - F(x).

   Input Parameters:
.  ts - the TS context
.  U - input vector
.  Udot - input vector
.  ptr - optional user-defined context, as set by TSSetRHSFunction()

   Output Parameter:
.  F - function vector
 */
PetscErrorCode IFunction(TS ts,PetscReal ftime,Vec U,Vec Udot,Vec F,void *ptr)
{
  AppCtx         *appctx = (AppCtx*)ptr;
  DM             da;
  PetscInt       i,j,Mx,My,xs,ys,xm,ym;
  PetscReal      hx,hy,sx,sy;
  PetscScalar    uc,uxx,uyy,vc,vxx,vyy;
  Field          **u,**f,**udot;
  Vec            localU;

  PetscFunctionBegin;
  PetscCall(TSGetDM(ts,&da));
  PetscCall(DMGetLocalVector(da,&localU));
  PetscCall(DMDAGetInfo(da,PETSC_IGNORE,&Mx,&My,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE));
  hx = 2.50/(PetscReal)Mx; sx = 1.0/(hx*hx);
  hy = 2.50/(PetscReal)My; sy = 1.0/(hy*hy);

  /*
     Scatter ghost points to local vector,using the 2-step process
        DMGlobalToLocalBegin(),DMGlobalToLocalEnd().
     By placing code between these two statements, computations can be
     done while messages are in transition.
  */
  PetscCall(DMGlobalToLocalBegin(da,U,INSERT_VALUES,localU));
  PetscCall(DMGlobalToLocalEnd(da,U,INSERT_VALUES,localU));

  /*
     Get pointers to vector data
  */
  PetscCall(DMDAVecGetArrayRead(da,localU,&u));
  PetscCall(DMDAVecGetArray(da,F,&f));
  PetscCall(DMDAVecGetArrayRead(da,Udot,&udot));

  /*
     Get local grid boundaries
  */
  PetscCall(DMDAGetCorners(da,&xs,&ys,NULL,&xm,&ym,NULL));

  /*
     Compute function over the locally owned part of the grid
  */
  for (j=ys; j<ys+ym; j++) {
    for (i=xs; i<xs+xm; i++) {
      uc        = u[j][i].u;
      uxx       = (-2.0*uc + u[j][i-1].u + u[j][i+1].u)*sx;
      uyy       = (-2.0*uc + u[j-1][i].u + u[j+1][i].u)*sy;
      vc        = u[j][i].v;
      vxx       = (-2.0*vc + u[j][i-1].v + u[j][i+1].v)*sx;
      vyy       = (-2.0*vc + u[j-1][i].v + u[j+1][i].v)*sy;
      f[j][i].u = udot[j][i].u - ( appctx->D1*(uxx + uyy) - uc*vc*vc + appctx->gamma*(1.0 - uc));
      f[j][i].v = udot[j][i].v - ( appctx->D2*(vxx + vyy) + uc*vc*vc - (appctx->gamma + appctx->kappa)*vc);
    }
  }
  PetscCall(PetscLogFlops(16.0*xm*ym));

  /*
     Restore vectors
  */
  PetscCall(DMDAVecRestoreArrayRead(da,localU,&u));
  PetscCall(DMDAVecRestoreArray(da,F,&f));
  PetscCall(DMDAVecRestoreArrayRead(da,Udot,&udot));
  PetscCall(DMRestoreLocalVector(da,&localU));
  PetscFunctionReturn(0);
}

PetscErrorCode IJacobian(TS ts,PetscReal t,Vec U,Vec Udot,PetscReal a,Mat A,Mat BB,void *ctx)
{
  AppCtx         *appctx = (AppCtx*)ctx;     /* user-defined application context */
  DM             da;
  PetscInt       i,j,Mx,My,xs,ys,xm,ym;
  PetscReal      hx,hy,sx,sy;
  PetscScalar    uc,vc;
  Field          **u;
  Vec            localU;
  MatStencil     stencil[6],rowstencil;
  PetscScalar    entries[6];

  PetscFunctionBegin;
  PetscCall(TSGetDM(ts,&da));
  PetscCall(DMGetLocalVector(da,&localU));
  PetscCall(DMDAGetInfo(da,PETSC_IGNORE,&Mx,&My,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE));

  hx = 2.50/(PetscReal)Mx; sx = 1.0/(hx*hx);
  hy = 2.50/(PetscReal)My; sy = 1.0/(hy*hy);

  /*
     Scatter ghost points to local vector,using the 2-step process
        DMGlobalToLocalBegin(),DMGlobalToLocalEnd().
     By placing code between these two statements, computations can be
     done while messages are in transition.
  */
  PetscCall(DMGlobalToLocalBegin(da,U,INSERT_VALUES,localU));
  PetscCall(DMGlobalToLocalEnd(da,U,INSERT_VALUES,localU));

  /*
     Get pointers to vector data
  */
  PetscCall(DMDAVecGetArrayRead(da,localU,&u));

  /*
     Get local grid boundaries
  */
  PetscCall(DMDAGetCorners(da,&xs,&ys,NULL,&xm,&ym,NULL));

  stencil[0].k = 0;
  stencil[1].k = 0;
  stencil[2].k = 0;
  stencil[3].k = 0;
  stencil[4].k = 0;
  stencil[5].k = 0;
  rowstencil.k = 0;
  /*
     Compute function over the locally owned part of the grid
  */
  for (j=ys; j<ys+ym; j++) {

    stencil[0].j = j-1;
    stencil[1].j = j+1;
    stencil[2].j = j;
    stencil[3].j = j;
    stencil[4].j = j;
    stencil[5].j = j;
    rowstencil.k = 0; rowstencil.j = j;
    for (i=xs; i<xs+xm; i++) {
      uc = u[j][i].u;
      vc = u[j][i].v;

      /*      uxx       = (-2.0*uc + u[j][i-1].u + u[j][i+1].u)*sx;
      uyy       = (-2.0*uc + u[j-1][i].u + u[j+1][i].u)*sy;

      vxx       = (-2.0*vc + u[j][i-1].v + u[j][i+1].v)*sx;
      vyy       = (-2.0*vc + u[j-1][i].v + u[j+1][i].v)*sy;
       f[j][i].u = appctx->D1*(uxx + uyy) - uc*vc*vc + appctx->gamma*(1.0 - uc);*/

      stencil[0].i = i; stencil[0].c = 0; entries[0] = -appctx->D1*sy;
      stencil[1].i = i; stencil[1].c = 0; entries[1] = -appctx->D1*sy;
      stencil[2].i = i-1; stencil[2].c = 0; entries[2] = -appctx->D1*sx;
      stencil[3].i = i+1; stencil[3].c = 0; entries[3] = -appctx->D1*sx;
      stencil[4].i = i; stencil[4].c = 0; entries[4] = 2.0*appctx->D1*(sx + sy) + vc*vc + appctx->gamma + a;
      stencil[5].i = i; stencil[5].c = 1; entries[5] = 2.0*uc*vc;
      rowstencil.i = i; rowstencil.c = 0;

      PetscCall(MatSetValuesStencil(A,1,&rowstencil,6,stencil,entries,INSERT_VALUES));
      if (appctx->aijpc) {
        PetscCall(MatSetValuesStencil(BB,1,&rowstencil,6,stencil,entries,INSERT_VALUES));
      }
      stencil[0].c = 1; entries[0] = -appctx->D2*sy;
      stencil[1].c = 1; entries[1] = -appctx->D2*sy;
      stencil[2].c = 1; entries[2] = -appctx->D2*sx;
      stencil[3].c = 1; entries[3] = -appctx->D2*sx;
      stencil[4].c = 1; entries[4] = 2.0*appctx->D2*(sx + sy) - 2.0*uc*vc + appctx->gamma + appctx->kappa + a;
      stencil[5].c = 0; entries[5] = -vc*vc;
      rowstencil.c = 1;

      PetscCall(MatSetValuesStencil(A,1,&rowstencil,6,stencil,entries,INSERT_VALUES));
      if (appctx->aijpc) {
        PetscCall(MatSetValuesStencil(BB,1,&rowstencil,6,stencil,entries,INSERT_VALUES));
      }
      /* f[j][i].v = appctx->D2*(vxx + vyy) + uc*vc*vc - (appctx->gamma + appctx->kappa)*vc; */
    }
  }

  /*
     Restore vectors
  */
  PetscCall(PetscLogFlops(19.0*xm*ym));
  PetscCall(DMDAVecRestoreArrayRead(da,localU,&u));
  PetscCall(DMRestoreLocalVector(da,&localU));
  PetscCall(MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY));
  PetscCall(MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY));
  PetscCall(MatSetOption(A,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE));
  if (appctx->aijpc) {
    PetscCall(MatAssemblyBegin(BB,MAT_FINAL_ASSEMBLY));
    PetscCall(MatAssemblyEnd(BB,MAT_FINAL_ASSEMBLY));
    PetscCall(MatSetOption(BB,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE));
  }
  PetscFunctionReturn(0);
}